where \(h_{k}\)  is given by (REF ). Inserting the above result into (REF ), the remaining summation over \(k\)  is evaluated by repeated use of the identity eq:B1 as well as the result [1]}
\(\psi _{0}(mk)=\ln m+\frac{1}{m}\sum _{i=0}^{m-1}\psi _{0}\left(k+\frac{i}{m}\right), \qquad m\in \mathbb {Z^{+}}.\) 
